The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  0  1  1  X  0  X  1  1  1  1  0  1  1  1  0  X  0  1  0  1  1  1  1  X  1  1  1  1  X  1
 0  X  0 X+2  0 X+2  0 X+2  2 X+2  0 X+2  0 X+2  2  X  0  0 X+2 X+2  2  2  X X+2 X+2 X+2  X  X  X  X X+2  X X+2  0  2  2  2  X  0 X+2  0  X X+2  X  2  X  0 X+2  0  2 X+2  0 X+2 X+2 X+2  0  0
 0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  0  0  0  2  2  0  2  0  2  2  2  2  0  0  2  2  0  0  2  0  0  0  2  2  2  2  2  0  0  0  2  2  2  0  2  0  0  0  2  0  0
 0  0  0  2  0  0  0  0  0  0  0  2  0  2  0  2  2  2  0  2  2  2  0  2  2  0  0  2  2  0  0  2  2  2  2  0  2  0  0  0  0  2  2  2  0  0  0  2  2  2  2  2  0  0  0  0  0
 0  0  0  0  2  0  0  0  0  0  2  0  2  0  2  0  2  0  2  2  0  0  2  2  2  2  2  2  2  2  2  2  2  2  0  2  2  2  2  0  2  2  0  0  2  0  0  2  2  2  2  0  0  2  2  0  0
 0  0  0  0  0  2  0  0  0  2  2  2  0  0  2  2  0  2  2  2  0  2  2  2  2  2  0  0  2  0  0  0  0  0  0  2  2  0  0  2  2  2  2  0  0  0  2  0  0  2  0  0  0  2  0  0  0
 0  0  0  0  0  0  2  0  2  0  2  2  0  2  2  0  0  2  0  0  0  0  2  0  2  2  2  0  2  0  0  2  2  0  2  2  0  0  2  0  0  2  0  2  2  0  2  0  2  2  0  0  2  2  2  0  0
 0  0  0  0  0  0  0  2  0  2  2  0  2  2  0  2  0  0  0  0  2  2  0  0  2  2  2  2  2  2  0  0  2  2  0  0  0  0  2  0  2  2  2  2  2  2  2  0  0  2  2  0  0  2  2  2  0

generates a code of length 57 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+26x^48+12x^49+66x^50+52x^51+79x^52+122x^53+148x^54+202x^55+221x^56+242x^57+195x^58+210x^59+130x^60+126x^61+70x^62+46x^63+34x^64+10x^65+25x^66+2x^67+13x^68+6x^70+5x^72+2x^76+1x^80+1x^82+1x^90

The gray image is a code over GF(2) with n=228, k=11 and d=96.
This code was found by Heurico 1.16 in 0.388 seconds.